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arXiv · 2306.11799

Obstructions to applying the Baker--Bilu method for determining integral points on curves

Aaron Landesman·Bjorn Poonen
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Abstract

We prove that for every smooth projective integral curve $X$ of genus at least $2$ over $\mathbb C$, there exists $x \in X(\mathbb C)$ such that no connected finite \'etale cover of $X-\{x\}$ admits a nonconstant morphism to $\mathbb G_m$. This has implications for the applicability of Baker's method to determining integral points on curves.

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Aaron Landesman, Bjorn Poonen. 2023-06-20. Obstructions to applying the Baker--Bilu method for determining integral points on curves. https://arxiv.org/abs/2306.11799

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